Question

The displacement ${}^{\prime }{x}^{\prime }$ (in meter) of a particle of mass ${}^{\prime }{m}^{\prime }$ (in $kg$) moving in one dimension under the action of a force, is related to time ${}^{\prime }{t}^{\prime }$ (in sec) by $t=\sqrt{x}+3$. The displacement of the particle when its velocity is zero, will be

• A. 4 m
• B. 0 m (zero)
• C. 6 m
• D. 2 m

Answer 1

Answer: (B)

Given : $t=\sqrt{x}+3$
or $\sqrt{x}=t-3$
Squaring both sides, we get
$x=(t-3{)}^2$
Velocity, $v=\frac{dx}{dt}=\frac{d}{dt}(t-3{)}^2=2(t-3)$
Velocity of the particle becomes zero, when
$2(t-3)=0$
or $t=3s$
At $t=3s$
$x=(3-3{)}^2=0m$